Creating dynamic leakage-free paths using coarse-graining techniques in the presence of decoherence

We present a method aimed at protecting unitary dynamics in the presence of decoherence, by integrating leakage elimination operators (LEOs) into the system's evolution to create dynamical leakage-free paths. Deriving the dynamical equation for an open quantum system with general drives can be challenging. Our approach avoids the rotating wave approximation and instead uses the coarse-grained averaging technique to derive a quantum master equation for such systems. The combination of the coarse-graining approach and LEO operators appears suitable to study Markovian control methods. We show that employing LEO pulses in specific subspaces can reduce errors arising from undesired transitions due to decoherence. Notably, satisfactory final fidelity can still be achieved even when the reservoir is at a finite temperature. By looking into the dynamical equation governing the quantum state on the dynamical leakage-free path, we provide analytical insights into the effectiveness of the LEO method in suppressing decoherence effects.